Question

7. A 50 kg athlete runs and grabs a 10.0 m rope and swings to a maximum height of 1.8 m above

the ground. A second athlete, who has a mass of 100. kg runs at the same speed, v, and grabs a
5.0 m rope. What maximum height will the 100. kg athlete swing to? Assume the mass of the
ropes and air resistance are negligible. Support your answer with calculations and/or a proof.
(3 marks)
50 kg
10 m
100 kg
T
5m

Answer 1

1.8 m

Step-by-step explanation:

All the KE of the 50 kg runner converts to PE at the top of his swing.

1/2mv² = mgh

1/2(50 kg)(v²) = (50 kg)(9.8 m/s²)(1.8 m)

25v² = 882

v² = 882/25 = 35.3

v = √35.3 = 5.94 m/s

The 100 kg runner also runs at the same speed, 5.94 m/s.

You can solve for the max. height (h) of the 100 kg runner:

1/2 (100 kg)(5.95 m/s)² = (100 kg)(9.8 m/s²)(h)

h = 1764.2/980 = 1.8 m SAME AS THE OTHER RUNNER!